Answers
Answer:
114126Step-by-step explanation:
The given expression describes the GP with
The first term:
t = 80(1.23²⁻²) = 80(1.23⁰) = 80The common ratio:
r = 1.23It is required to find the sum of the terms from 2 (the bottom number of sigma) through 29 (the top number of sigma)
The number of terms is
n = 29 - 2 + 1 = 28The sum of the first 28 terms is
Sₙ = t(rⁿ - 1)/(r - 1) S₂₈ = 80(1.23²⁸ - 1)/(1.23 - 1) = 114125.75573 ≈ 114126 (rounded)Answer:
114,126 (nearest whole number)
Step-by-step explanation:
Geometric sequence
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
Given:
[tex]\displaystyle \sum^{29}_{n=2}80(1.23)^{n-2}[/tex]
The sigma notation means to find the sum of the given geometric series where the first term is when n = 2 and the last term is when n = 29.
First term (a)
Determine the first term by substituting n = 2 into the given expression:
[tex]n=2 \implies 80(1.23)^{2-2}=80[/tex]
Common ratio (r)
From inspection, the common ratio is 1.23.
nth term
As the first term is when n = 2 and the last term is when n = 29, there is a total of 28 terms.
Therefore:
a = 80r = 1.23n = 28Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Substituting the given values into the formula:
[tex]\implies S_{28}=\dfrac{80\left(1-1.23^{28}\right)}{1-1.23}=114125.7556[/tex]
Therefore, the sum of the given geometric series is 114,126 (nearest whole number)
Related Questions
What is the circumference of the following circle? Diameter=3 Radius=1.5
Answers
Answer: 3π in terms of pi or 9.42 if in π or pi= 3.14
Step-by-step explanation:
solve 3y= x+1 and 2y= x
Answers
Answer:
(2, 1 )
Step-by-step explanation:
3y = x + 1 → (1)
2y = x → (2)
substitute 2y = x into (1)
3y = 2y + 1 ( subtract 2y from both sides )
y = 1
substitute y = 1 into either of the 2 equations and solve for x
substituting into (2)
2(1) = x
2 = x
solution is (2, 1 )
Answer:
{y,x} = {-1,-2}
Step-by-step explanation:
2y = - 2
[2] y = - 1
// Plug this in for variable y in equation [1]
[1] 3•(-1) - x = -1
[1] - x = 2
// Solve equation [1] for the variable x
[1] x = - 2
// By now we know this much :
y = -1
x = -2
{y,x} = {-1,-2}
hope this helps
pls mark brainliest
Illustrate on a number line the solution set of each pair of simultaneous inequalities. x>-2;-4 <x <2
Answers
The intersection region will be between -2 <x <2 or x ∈ (-2, 2) if the two inequalities are x>-2 and -4 <x <2
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have two inequalities:
x>-2 and
-4 <x <2
or
x ∈ ( -2, ∞) and x ∈ (-4, 2)
The intersection region will be(from the graph)
x ∈ (-2, 2)
Thus, the intersection region will be between -2 <x <2 or x ∈ (-2, 2) if the two inequalities are x>-2 and -4 <x <2
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Write a 2nd degree equation whose solutions are 5+✓(11) and 5-✓(11)
Answers
Answer:
For each object, choose an appropriate scale for a drawing that fits on a regular sheet of paper. Not all of the scales on the list will be used.
Step-by-step explanation:
This is the question picture
Answers
Answer:
A = X
B=Z
C=Y
Step-by-step explanation:
As they are congruent, their corresponding angles are also congruent
Answer:
a)
angle a is congruent to angle x
angle b is congruent to angle z
angle c is congruent to angle y
b)
line ab is congruent to line xz
line ac is congruent to line xy
line bc is congruent to line zy
c)
triangle bca is congruent to triangle zyx
please help me I will give brainliest
Answers
Answer:
D
Step-by-step explanation:
um well just based on what its asking for it wants a sentence that uses both.
2. A sphere has a great circle whose circumference is 95 centimeters. Which of the following is closest to the
volume of the sphere, in cubic centimeters?
1) 4,600
(3) 12,700
2) 7,500
(4) 14,500
Answers
Answer:
Approximately [tex]14,\!500\; {\rm cm^{3}}[/tex].
Step-by-step explanation:
The radius of a sphere is the same as the radius of the great circle of that sphere.
Thus, in this question, it would be possible to find the radius of the sphere by finding the radius of the great circle.
The circumference of a circle of radius [tex]r[/tex] is [tex]2\, \pi \, r[/tex]. In this question, it is given that the circumference of this great circle is [tex]95\; {\rm cm}[/tex]. Thus, the radius of this great circle would be:
[tex]\begin{aligned}r &= \frac{95\; {\rm cm}}{2\, \pi} \approx 15.1197\; {\rm cm}\end{aligned}[/tex].
Thus, radius of the sphere in this question would also be approximately [tex]15.1197\; {\rm cm}[/tex].
The volume of a sphere of radius [tex]r[/tex] is [tex](4/3)\, \pi\, r^{3}[/tex]. Thus, the volume of this sphere of radius [tex]r = 15.1197\; {\rm cm}[/tex] would be approximately:
[tex]\begin{aligned}\frac{4}{3} \, \pi\times (15.1197\; {\rm cm})^{3} \approx 14,\!500 \; {\rm cm^{3}}\end{aligned}[/tex]
What is the perimeter of the triangle below?
48.0 units
14.7 units
16.7 units
24.0 units
Answers
Is anyone free to help?
Answers
Answer:
-4 C (Negative 4 C)
Step-by-step explanation:
If its 20 C less in Moscow, then it must be 16-20 = - 4 C in Moscow.
Look up rules on subtracting large numbers from small numbers to understand how I got - 4.
Moscow: 20 degrees colder
16-20= -4
A mean weight of 2.2 pounds is computed for a random sample of 50 catfish from a lake.
What can you infer from this random sample?
A)You infer that the mean weight of all catfish is close to 2.2 pounds.
B)You infer that the mean weight of all catfish is exactly to 2.2 pounds.
C)You infer that the mean weight of catfish in the lake is close to 2.2 pounds.
D)You infer that the mean weight of catfish in the lake is exactly to 2.2 pounds.
Answers
Answer:
C)
Step-by-step explanation:
It can't be A or B because the samples from 50 fish definitely wouldn't be equal to ALL the fish ever.
And it (more so) can't be D because you are finding the mean. that means that some catfish could weight 1 pound, and another could weigh 4, they would just cancel out.
That leaves C) with the only plausible answer.
Without considering other forces such as friction what is the net force in this problem?
Answers
Answer:
25 N to the left
Step-by-step explanation:
The net force is equal to the differences in magnitudes of the forces acting on it.
Take the left direction to be positive (+) and right direction to be negative (-).
Solving :
Net Force = Force (left) - Force (right)
Net Force = 10 + 20 - 5
Net Force = 30 - 5
Net Force = 25 N to the left
F_net
F1+F2+F310+20-530-525NCan anyone help me with this area of sector activity? I'm not sure how to solve this. I will reward brainliest! Please tell me how you got your answer as well! this is 10th grade geometry
Answers
Answer:
Jenny has worked out the area of the whole circle using the formula π × r² where r is the radius length. She has assumed π is 3.14 which leads to her working of 3.14 × 10² = 314 units². She has to divide the total area by 4 to calculate the sector area.
Let's check
Angle is 90°Radius is 10Area of sector
Ø/360×πr²90/360×pi(10)²1/4×π(100)25π78.5units²Find the surface area of the prism. Enter your answer in the box.
Answers
Answer:
Area of the prism = 2(lw + lh + wh)
l = length = 6 m
w = width = 3 m
h = height = 12 m
—
Area of the prism = 2(6*3 + 6*12 + 3*12) = 2(18 + 72 + 36) = 2(126) = 252 m²
—
Have a nice day!!
A box with square base and a height of 8cm has a volume of 1 332 cm3. find the length of the side base
Answers
Answer:
12.9 cm
Explanation:
Volume of rectangular box = Length × Width × Height
Given following:
Height = 8 cmConsider one of the base side as xSolve for volume:
L × W × H = Vx × x × 8 = 1332x² = 1332/8x = √166.5 ≈ 12.9 cmPlease help!!!!!!!! Thank you sooo much!
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
∠ XBC = 55° because it corresponds to ∠ AXY
(b)
since XB = XC then Δ XBC is isosceles with base angles congruent, that is
∠ XBC = ∠ XCB = 55°
the sum of the 3 angles in Δ XBC = 180° , then
∠ BXC + 55° + 55° = 180°
∠ XBC + 110° =180° ( subtract 110° from both sides )
∠ XBC = 70°
Carl is covering the rectangular prism-shaped
box with cloth.
5 in.
2 in.
-
12 in.
what is the minimum amount of cloth carl
needs to cover the entire box?
Answers
The minimum amount of cloth carl needs to cover the entire box will be 188 square inches.
What is a surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any object is called the surface area.
Given that:-
The length width and the height of the prism are 5 , 2 , and 12 inches respectively.The minimum amount of cloth carl needs to cover the entire box will be the surface area of the prism
Surface area = 2 [ (5 x 2)+ (12 x 5) + (12 x 2)]
Surface area= 188 square inches
Therefore the minimum amount of cloth carl needs to cover the entire box will be 188 square inches.
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Find the vertex. f(x)=2^2 - 8
Answers
Answer:
(0, -√2)
Step-by-step explanation:
Given :
f(x) = x² - 8Finding vertex :
Given by (h, k)h = -b/2a = 0k = -D/4aD = √0 - 4(1)(-8) = √32 = 4√2k = -4√2/4 = -√2Vertex is (0, -√2)what is the diffrence between -25 and -12
Answers
Calculate the difference between the two negative values
After you know the negative values you're comparing, you can calculate the difference. Do this by subtracting one negative value from the other. For example, you'd subtract -7 from -5 to get -2.
So (-25) - (-12) = -13
Why is apr an important tool for consumers
Answers
Answer:
APR, or annual percentage rate, is your interest rate stated as a yearly rate. An APR for a loan can include fees you may be charged, like origination fees. APR is important because it can give you a good idea of how much you'll pay to take out a loan.
Please help me! Im so confused. If you could explain, too that would be great!!! <3
Answers
Answer:
the base length is 8 units
Step-by-step explanation:
You can use pythagorean theorem to solve this
Question 3
ceiling fan the blades of a ceiling fan have a length of 26 inches. the tips of the blades follow a circular path. how far does the tip of a
blade travel in 1/5 of a rotation? round to the nearest hundredth of an inch,
________inches
Answers
The distance the blades travel in 1/5 of a rotation is 32.67 in
Since the distance the blades of the ceiling fan rotate is the length of an arc, we find this length
What is the length of an arc?The length of an arc is given by
L = Ф/360° × 2πr where
Ф = angle of rotation and r = length of blades of fanSince
Ф = 1/5 of a rotation = 1/5 × 360° = 72° and r = 26 inThe distance the blades travelSo, substituting the values of the variables into the equation, we have
L = Ф/360° × 2πr
L = 72°/360° × 2π × 26 in
L = 1/5 × 52π in
L = 10.4π in
L = 32.67 in
So, the distance the blades travel in 1/5 of a rotation is 32.67 in
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The perimeter of a rectangle is 22,411 inches. The width of the
rectangle is 260 inches. What is the length, in inches, of the rectangle?
Answers
Answer:
Step-by-step explanation:
P = perimeter of the rectangle; and w = width of the rectangle.Use the formula:
Length(L) = P/2 - wPlug In:
22,411 ÷ 2 - 260
Solve:
22,411 ÷ 2 = 11205.510945.5Answer is L = 10,945.5 inches
explain: perimeter is all 4 sides added together
We know one side is 260
we know the perimeter is 22,411
260 + 260 + L + L = 22,411
combine like terms
520 + 2L = 22,411
subtract 520 from both sides to isolate 2L
2L = 21,891
divide both sides by 2 to isolate L
L = 10,945.5 inches
Sean has 3 times as many vegetable plants as Liz and Sejuan combined. Liz has 3 vegetable plants, and Sejuan has 2 vegetable plants. How many vegetable plants does Sean have?
Which statements about this word problem are true? Check all that apply.
A: This is an example of a part-whole problem.
B: This is an example of a comparison problem.
C: Addition then multiplication can be used to solve the problem.
D: Subtraction then division can be used to solve the problem.
E: Division then multiplication can be used to solve the problem.
Answers
Answer:
C: Addition then multiplication can be used to solve the problem
Step-by-step explanation:
Help Find the unit rate.
4,928 rooms on 112 floors =
rooms per floor
Answers
4928 rooms / 112 floors
2464 rooms / 56 floors
---Really, all we are doing here is simplifying a fraction until we have a 1 in the denominator
44 rooms / 1 floor
Hope this helps!
Use the diagrams to determine which statements are true. Select all statements that are true.
Answers
Answer:
I don't see your questions.
Egypt. Africa. America
x² + y² = 34
=
y = x+2
Show your working.
Answers
Answer:
[tex]\left \{ {{y=5} \atop {x=3}} \right.[/tex] or [tex]\left \{ {{y=-3} \atop {x=-5}} \right.[/tex]
Step-by-step explanation:
Answer:
(- 5, - 3 ) , (3, 5 )
Step-by-step explanation:
x² + y² = 34 → (1)
y = x + 2 → (2)
substitute y = x + 2 into (1)
x² + (x + 2)² = 34
x² + x² + 4x + 4 = 34
2x² + 4x + 4 = 34 ( subtract 34 from both sides )
2x² + 4x - 30 = 0 ( divide through by 2 )
x² + 2x - 15 = 0 ← in standard form
(x + 5)(x - 3) = 0 ← in factored form
equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 3 = 0 ⇒ x = 3
substitute these values into (2) for corresponding values of y
x = - 5 : y = - 5 + 2 = - 3 ⇒ (- 5, - 3 )
x = 3 : y = 3 + 2 = 5 ⇒ (3, 5 )
Help on this math a s a p if possible
Answers
Answer:
Mean - 17.222222222222
Median - 17
Mode - 12
Step-by-step explanation:
lets arrange this is least to greatest.
2, 4, 12, 12, 17, 18, 28, 29, 33
to find the mean(even though you dont need it), you add all the numbers up and devide by the amount of numbers.
so -> 2 + 4 + 12 + 12 + 17 + 18 + 28 + 29 + 33 = 155
and there are 9 numbers, so 155 / 9 = 17.2 and a lot more 2s
to find the median, you arrange from least to greatest vice versa, then find the middle number.
2, 4, 12, 12, 17, 18, 28, 29, 33
the middle number is 17, so the mean is 17
to find the mode, you have to find the number that is most repeated.
2, 4, 12, 12, 17, 18, 28, 29, 33
the number that is repeated the most is 12, so your mode is 12.
Hope this helped!!!
Help please right now you will get thanks and brainlest and 25 points it's due at 9
Answers
Answer:
B.
Step-by-step explanation:
Answer:
See below ~
Step-by-step explanation:
Question 4
P(6) = Number of 6 rolled / Total rollsP(6) = 10/50P(6) = 1/5 = 0.2 = 20% [A, B, and E]Question 11
Part A
The complement of the event is all of the unlikely possibilitiesBasically everything other than rolling a 4[A, B, C, E, and F]Part B
P' (4) = 1 - P (4)P' (4) = 1 - 1/6P' (4) = 5/6
What is the approximate circumference of the circle that has a center (3, 1) and passes through the point (3, 4)?
Answers
Step-by-step explanation:
You use the Distance Formula
d= √( x2 - x1 )^2 + ( y2 - y1 )^2
substitute
r= √(3-3)^2 + (4-1)^2
√0^2 + 3^2
r = √9
r = 3
Now you can use the equation for finding the circumference
2πr
2π3
≈ 6π or 18.85
Greta is painting two different rectangular prisms. The prisms have the following dimensions.
Prism A:
Length: 1 foot
Width: 4 inches
Height: 8 inches
Prism B:
Length: 10 inches
Width: 2 inches
Height: 1.5 feet
Which prism has a greater surface area, and what is its surface area in square inches?
Answers
Answer:
prism B is greater
Step-by-step explanation:
prism A
lenght: 1×4=4
width: 4×8=32
height: 8×1=8
add them all up and multiply it by 2 = 4+32+8×2=52
prism B
lenght: 10×2=20
width: 2×1.5=3
height:1.5×10=15
add them all up and multiply it by 2= 20+3+15×2=76